Why Random Matrices can Change the Future of Research in AI?

Abstract: Machine learning and AI algorithms are becoming increasingly more powerful but also increasingly more complex, mathematically less tractable, and energetically less environmental friendly. In this talk, we will demonstrate that large dimensional statistics, and particularly random matrix theory, simultaneously (i) explains why ML algorithms are so stable when dealing with large dimensional data, (ii) manages to break the difficulties that make these algorithms mathematically intractable (non-linearities and data modelling), thereby (iii) allowing for the first time to get (iii-a) an inside understanding of the algorithms, of their multiple biases and, most crucially, of their quite counter-intuitive behavior as well as (iii-b) a toolbox to easily improve the algorithms performance and cost efficiency. Possibly even more surprisingly, the universality notion in random matrix theory shows (iv) why ML algorithms applied to intricate real data (in general impossible to model) behave the same as when applied to elementary Gaussian random vector models.

The course will introduce basic notions of random matrix theory by emphasizing on the counter-intuitive behavior of large dimensional data (so to raise awareness in the audience). These notions will be applied to a range of telling applications in machine learning (spectral clustering, semi-supervised learning, transfer learning, low-cost processing, etc.).

The audience can dynamically decide on which topic they'd like me to cover preferably. A time for debate will also be given for the audience to react on the presentation. An extensive coverage of the class material is available online in the upcoming book “Romain COUILLET, Zhenyu LIAO, “Random Matrix Theory for Machine Learning” romaincouillet.hebfree.org/book.html

statistical mechanicsmathematical physicsprobability

Audience: advanced learners

Séminaire MEGA

Series comments: Description: Monthly seminar on random matrices and random graphs